Tools are known, for example from U.S. Pat. Nos. 4,468,623, 6,600,321, 6,714,014 or 6,809,521 using current injection measurements in order to obtain micro-electric images of a borehole wall, the borehole penetrating geological formations.
FIG. 1A is a partial cross-section view in a borehole BH showing a part of a typical high-frequency current injection tool TL according to the hereinbefore mentioned prior art. The tool TL is comprised in a string of tool TS. The tool TL comprises a current injection section CIS and a current return section CRS. The current injection section CIS is isolated from the current return section CRS by an isolation section ISS. The current injection section CIS comprises a pad P carrying electrodes for injecting a survey current IS into the geological formations when the pad P1 contacts the borehole wall BW. A current source or voltage source SC is connected between the current injection section and the current return section such that the current injection section CIS is driven at a voltage V=V0(t) with respect to the current return section CRS. Generally, the current source or the voltage source is not an ideal source and is positioned in a middle location between the current injection section and the current return section. The electrode(s) is (are) held at approximately the same electric potential (voltage) as the current injection section. The survey current IS is a three dimension current tube connecting the electrode and a portion of the current return section.
When the borehole is filled with a conductive mud, e.g. a water-base mud, such tools normally operate at low frequencies, e.g. below 20 kHz. In conductive mud, the interpretation of the measured current is easily related to the local resistivity of the borehole wall.
When the borehole is filled with a non-conductive/resistive mud, e.g. an oil-base mud, such tools operate at high frequencies, e.g. above around 100 kHz. FIGS. 1B and 1C schematically show approximate equivalent circuit models in such a case. In non-conductive/resistive mud the survey current IS is controlled by the impedance of the mud ZMD, the impedance of the formation ZGF and the impedance of the current return ZCR, combined in series. The impedance of the mud ZMD is the impedance between the current injection section CIS (more precisely point A) and the geological formation GF (more precisely point B). The impedance of the mud ZMD is defined as ZMD=VAB/IS, where VAB is the complex voltage between points A and B and IS is a complex quantity. The impedance of the formation ZGF is defined by the impedance between point B and point C. The impedance of the formation ZGF is defined as ZGF=VBC/IS, where VBC is the complex voltage between points B and C. The impedance of the current return ZCR is the impedance between the geological formation GF (more precisely point C) and the current return section CRS (more precisely point D). The impedance of the current return ZCR is defined as ZCR=VCD/IS, where VCD is the complex voltage between points C and D. The tools of the prior art as hereinbefore mentioned use as a current return the whole string of tools above the insulation section over which a voltage drop is applied (from V=V0 to V=0). If the mud impedance ZMD is significantly greater than the formation impedance ZGF then the measurement is insensitive to the formation impedance ZGF. In this case a higher frequency is needed to reduce the mud impedance ZMD, by the capacitive effect, so that the formation impedance ZGF can be measured. However, it is observed that the impedance of the current return ZCR at high frequency still affects the current measurement.
At high frequencies, the wavelength is short and becomes comparable to or smaller than the tool string length. Typically, the tool string being conductive, the mud around being resistive and the geological formations being conductive, they define a coaxial wave-guide/cable with the tool string as the inner conductor and the formation as the outer conductor. From transmission-line theory, it is known that the complex impedance of the coaxial wave-guide/cable at the input depends highly on the length of the coaxial wave-guide/cable. Generally, the impedance of the current return ZCR may be approximated by various capacitances C0, C1, C2, etc. . . . and inductances L1, L2, L3, etc. . . . combined in parallel depending on the locations at which the string of tools TS touches or at least has a good electrical contact with the borehole wall BW. In the approximate equivalent circuit model of FIG. 1C, a good electrical contact at positions P1 and P2 is represented by a switch S1, S2 associated with the respective capacitance that is closed. In the example of FIG. 1C, none, one or both switches S1, S2 may be closed. It is difficult to determine the exact position where the string of tools touches the borehole wall or has the best electrical contact to the geological formations. Consequently, at high frequency, with a borehole filled with a non-conductive/resistive mud surrounded by a lower resistance geological formation, the impedance of the current return ZCR may vary strongly when the tool measures survey currents IS, thus significantly influencing these measurements. Therefore, the tools according to the hereinbefore mentioned prior art may have an insufficient accuracy.